Say you alloca(1GB), and alloca() is naive and gives it to you even though that 1GB spans several other stacks, and now you write somewhere in the middle. If you're lucky you'll hit unmapped space and trigger a segfault. If you're unlucky you'll scribble over another thread's stack or whatever.
But if you progressively write into the alloca()ed area in the direction of stack growth then you cannot corrupt other mappings, and you can only segfault if you exceed your stack's maximum size. Of course, there can be platforms with no SIGSEGV or whatever.